1. Field of the Invention
This invention relates to a four-wave mixing method for generating a phase conjugate wave by using a photorefractive effect of a photo-nonlinear medium. In particular, it relates to a method of measuring the time for forming a refractive index grating of a photo-nonlinear medium in accordance with a method of mixing four-waves.
2. Description of the Related Art
As shown in FIG. 5, a four-wave mixing device includes a photo-nonlinear medium 1 made of photorefractive crystal. Both opposing surfaces of the photo-nonlinear medium 1 are formed thereon with light incident surfaces 1a and 1b. A pair of external electrodes 1c and 1d are provided on both opposing surfaces in the orthogonal direction to the normal direction of the light incident surfaces 1a and 1b. Numerals 2 and 3 depict first and second pump beams respectively, 4 a probe beam, and 5 a phase conjugate wave generated by four-wave mixing. The probe beam 4 and the first pump beam 2 form a specified angle .theta. therebetween to be incident on light incident surface 1a of the photo-nonlinear medium 1; the second pump beam 3 travels on the same optical path as, and in the opposing direction to, the first pump beam 2 and is incident on light incident surface 1b.
The first pump beam 2 and probe beam 4 are incident on the light incident surface la of the photo-nonlinear medium 1 to produce light interference fringes in the normal direction of the light incident surface. The light interference fringes form a refractive index grating 6.
A process of forming the refractive index grating 6 is explained in the following. In the photorefractive crystal, there is provided a level at which an impurity or the like acts as a donor or an acceptor each having electrical charges. As shown in FIG. 6(a), if a light interference between the first pump beam 2 and the probe beam 4 provides a pattern of light contrast, i.e., the interference fringes in the crystal, then electric charges, for example, electrons at a bright portion, are excited to a conducting band. When the external electric field is not applied on the crystal, the electrons are diffused in the conducting band s shown in FIG. 6(b) and trapped at the other level to reduce a space charge distribution as shown in FIG. 6(c). In such a case, the external electric field is applied through the electrodes 1c and 1d provided on the crystal. The electrons thus excited must drift to obtain a larger moving distance.
As in the foregoing arrangement, the space charge distribution produced in the crystal along the direction "x" induces a partial space electric field E, where a change of refractive index arises by Pockels effect caused by such electric field. The charge .rho. is satisfied by the following equation: EQU dE/dx =-.rho. (1)
In the case where the electrons are diffused to move, the refractive index grating 6 formed by the refractive index change is shifted in its phase by .pi./2 relative to a light intensity distribution (contrast of light). On the other hand, from the process of drifting due to the external electric field, the refractive index grating 6 and the light intensity distribution both come into phase with each other. In this way, a phenomenon where the refractive index is changed by irradiation of light on the crystal is called a photorefractive effect.
In the case where optical frequencies .omega. of the probe beam 4 and the pump beams 2 and 3 are made equal to each other and another coherent second pump beam 3 is incident on the refractive index grating 6 through the light incident surface 1b, then the second pump beam 3 is diffracted by the refractive index grating 6, the diffracted beam 5 travels in the reverse direction on the incident optical path of the probe beam 4. Such diffracted beam 5 is a phase conjugate wave having the same optical frequency .omega.(phase) as those three waves of the probe beam 4 and pump beams 2 and 3, and having a relationship of being a complex conjugate with an electric field amplitude of the probe beam 4.
The phase conjugate wave 5 reversely travels exactly along the optical path followed by the probe beam 4. Accordingly, by using such characteristic, consideration is provided for various utilizations such as in a real-time hologram and an image recovery. However, in the four-wave mixing method using the photorefractive effect, a reflection factor of the phase conjugate wave is relatively low. To raise the reflection factor of the phase conjugate wave, for the four-wave mixing devices of this kind there have been proposed a moving grating method of moving the refractive index grating 6 and the interference fringes respectively in the photorefractive crystal as described in the following documents:
1. J. P. Huignard, et. al., Optics Communications 38,249 (1981), PA1 2. N. Nuktarev, et. al., Ferroelectrics 22,949 (1979). PA1 3. H. Rajbenback, et. al., Optics Letters, 9, 558 (1984). PA1 4. J. P. Huignard, et. al., Appl. Optics 24, 4285 (1985).
FIG. 7 is an example of the four-wave mixing device based on the moving grating method. In FIG. 7, the same or corresponding parts as in FIG. 5 are designated by the same symbols and numerals. An optical path of the first pump beam 2 is provided with a reflection mirror 8 mounted with a piezoelectric oscillator 7. A voltage signal of sawtooth waveform is input to the piezoelectric oscillator 7 to drive the reflection mirror 8, the first pump beam 2 is then shifted (Doppler shifted) by a frequency determined depending on the sawtooth shaped waveform.
In this device, electrons excited responsive to the intensity distribution of the interference fringes produced by the first pump beam 2 and the probe beam 4 are caused to drift by a direct-current electric field applied on the electrodes 1c and 1d of the photo-nonlinear medium 1. These electrons form the refractive index grating in the crystal of the photo-nonlinear medium 1 through the space electric field and contribute to a generation of the phase conjugate wave 5. When the frequency of the first pump beam 2 is slightly modulated (Doppler shifted) by the reflection mirror 8, the interference fringes can thus be moved at a constant speed.
These interference fringes require a constant response time between the instant of starting its formation in the crystal and the instant of beginning its production of the refractive index distribution. For example, in an arrangement of a photo-nonlinear medium Bi.sub.12 SiO.sub.20 (hereinafter, simply referred to as "BSO"), such response time ranges from several tens ms to several hundreds ms. Accordingly, with the interference fringes being moved at a constant speed, a phase difference has resultantly been produced because the interference fringes which have formed the refractive index grating had been moved at the time that such the refractive index grating has been made up. A moving speed of the interference fringes is determined depending on an amount of modulation of an optical frequency. Therefore, an optimum phase difference can be obtained by varying an extent of the modulation. This thus results in raising a reflection factor of the phase conjugate wave.
On the other hand, the time required for forming the refractive index grating by the interference fringes of the photo-nonlinear medium is a basically important property of matter together with density of charges, mobility, diffusion coefficient, trap density, and donor acceptor density of the photorefractive crystal. For example, to apply the photo-nonlinear medium to the real-time hologram using the four-wave mixing method and the like, the time required for forming the refractive index grating is an extremely significant parameter for determining the time required for the operating process of the real-time hologram and the speed of the photo-nonlinear device.
Conventionally, the forming time of the refractive index grating has been measured by a birefringence method using a Senaramonte method etc. Such measurement, however, requires a considerably long time because of the complicated optical system. Further, the photo-nonlinear medium with an isotropy such as BSO of a cubic system can not be applied by the birefringence method because it has no birefringence, hence a method of measuring the time for forming the refractive index grating has not yet been established.